Bridge cables submitted to wind, rain, traffic and (more rarely) to earthquakes exhibit important motions sometime in correspondence of the deck oscillations. The resonance phenomena are responsible of these dangerous motions which conduct to fatigue damages and in the worst cases to cable rupture or bridge collapse in extreme situations. The resonance phenomena may be defined as “every particle is in synchronous harmonic motion with the same frequency”. The resonance is the tendency of a system to oscillate at greater amplitude at some frequencies than others. The resonance occurs when the input energy focuses mainly on one mode of vibration of the structure which means at one particular value of period of oscillation. After each new period of time the input energy is summed to the previous one. This summation conducts to reach high level of vibrations called resonance. Thus, the vibrations of the cables may have very deleterious consequences for the bridge. In view of this, several solutions have been considered and proposed for reducing or preventing (excessive) vibrations of cables.
Most of the solutions provided are based on the same concept, which is generally called damping. The damping corresponds to any effect that tends to reduce the amplitude of oscillations in an oscillatory system, acting on the consequences of the resonance phenomena but not on the causes. The damping may be explained in term of energy. The input energy (such as vibrations caused by wind, rain, earthquakes or traffic) causes structural motions (vibrations), which can be measured by the kinetic energy of the structure. By connecting some devices, called dampers, to the cables, a part of the kinetic energy will be degraded to heat inside these devices by different mechanisms. A damper is a device that deadens, restrains or depresses the vibrations of the cable. In this way, energy is removed from the main structure to the damper where viscous fluid, or visco-elastic materials, or magneto-rheological or hysteretic materials, converts the energy. With the damping method, the shape of the dynamic motion is unchanged but the amplitude of the modes is reduced by the damping effected by the devices. Most of the dampers used are passive devices, due to their practical application, their reduced cost and their robustness. In the case of cables, the dampers are inserted most often close from anchorage of the cables. This technique is rather simple but the efficiency due to their position on the cable is limited. The maximum damping increment factor is about 2 and for a few modes only. Another inconvenient is in some cases the aging of the dampers, as the material or liquid used is continuously working. Due to this problem, dampers must be replaced more than once in the structure's life when they become less efficient. Sometime, they are also invasive on the design of the bridge as they have generally important dimensions due to the forces they are submitted to near the anchorages.
In view of this, novel passive systems which also use the same damping process have been developed. Said novel passive systems involve the use of Shape Memory Alloy (SMA) materials, which are wires, made generally of Nickel, and Titanium. The interest with respect to the classical devices is essentially their minimum clutter. In these systems the damping comes from the hysteric behavior of Shape Memory Alloy material.
Furthermore, in the last decade, most of the passive solutions were improved drastically by introducing an active or a semi-active control of the dampers using different procedures and algorithms. These techniques brought different improvements in vibrations damping. However, the active and semi-active controls of the dampers are not easy to implement. In addition, they require an electrical power supply and electronic supports. Consequently, frequent maintenance is necessary and costs are increased which lets the bridge builder to still prefer passive solutions and to use the active and semi-active controls of the dampers for exceptional structures only.
Another type of solution named Tuned Mass Damper (TMD) could be used in some cases when the structure is submitted permanently to a given force which corresponds to one of the natural frequencies of the structure. By connecting a small mass via a spring to the structure it is possible to counteract a part of the structural motion by the small mass moving in opposition phase. In this way, a part of the energy is transferred to the new degree of freedom added to the structure. Two new modes appear instead of one, with smaller amplitudes, and generally a damper is associated to the mass added, to limit its motion. Thus, the mechanism generally involves a damper, which is associated to the mass added for limiting its motion. This mechanism is generally not applied on cables as the excitation spectra, most often large band, could excite one of the new modes created. These devices are applied more often on the bridges themselves under the deck when a particular frequency is expected. However, the drawbacks of theses devices relate to the added weight and to their location.
One further specific system used for cables is the cross tie tendons, which is made most often of steel rods or tendons connecting several cables together. The effect is to reduce drastically the vibrations amplitude of each single cable. The inconvenient are the new local modes between the ties, and the design of the cross ties which is not always easy to optimize. A further inconvenient is the aesthetic of the solution with respect the bridge design as the cross-ties work only if they are at the antinodes of the cable vibrations and therefore distant from the anchorages. Thus, this kind of device is visible and affects the design of the bridge.
As a result, there still is a need to develop a new method for protecting taut cables that efficiently neutralizes the vibrations, which does not require significant maintenance, and which does not involve the use of a device which is aesthetically too invasive.